The length of a rectangle is the sum of the width and 1. The area of the rectangle is 20 units. What is the width, in units, of the rectangle?

Width of the rectangle is 4 units

Step-by-step explanation:

Area of the rectangle = length × width

⇒ 20 = x (x + 1)

⇒ 20 = x² + x

⇒ x² + x - 20 = 0

⇒ x² + 5x - 4x - 20 = 0 (Using Product Sum rule to factorize)

⇒ x(x + 5) - 4(x + 5) = 0

⇒ (x + 5)(x - 4) = 0

⇒ x = -5, 4 (negative value is neglected)

x = 4

step-by-step explanation:

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.